Articoli correlati a Geometric Integration Theory
Sinossi
Geared toward upper-level undergraduates and graduate students, this treatment of geometric integration theory consists of three parts: an introduction to classical theory, a postulational approach to general theory, and a final section that continues the general study with Lebesgue theory.
The introductory chapter shows how the simplest hypotheses lead to the employment of basic tools. The opening third of the treatment, an examination of classical theory, leads to the theory of the Riemann integral and includes a study of smooth (i.e., differentiable) manifolds. The second part, on general theory, explores abstract integration theory, some relations between chains and functions, general properties of chains and cochains, and chains and cochains in open sets. The third and final section surveys Lebesgue theory in terms of flat cochains and differential forms, Lipschitz mappings, and chains and additive set functions. Appendixes on vector and linear spaces, geometric and topological preliminaries, and analytical preliminaries, along with indexes of symbols and terms, conclude the text.
The introductory chapter shows how the simplest hypotheses lead to the employment of basic tools. The opening third of the treatment, an examination of classical theory, leads to the theory of the Riemann integral and includes a study of smooth (i.e., differentiable) manifolds. The second part, on general theory, explores abstract integration theory, some relations between chains and functions, general properties of chains and cochains, and chains and cochains in open sets. The third and final section surveys Lebesgue theory in terms of flat cochains and differential forms, Lipschitz mappings, and chains and additive set functions. Appendixes on vector and linear spaces, geometric and topological preliminaries, and analytical preliminaries, along with indexes of symbols and terms, conclude the text.
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Contenuti
Preface Introduction A. The general problem of integration B. Some classical topics C. Indications of general theory Part I. Classical Theory 1. Grassmann algebra 2. Differential forms 3. Riemann integration theory 4. Smooth manifolds A. Manifolds in Euclidean space B. Triangulation of manifolds C. Cohomology in manifolds Part II. General Theory 5. Abstract integration theory 6. Some relations between chains and functions 7. General properties of chains and cochains 8. Chains and cochains in open sets Part III. Lebesgue Theory 9. Flat cochains and differential forms 10. Lipschitz mappings 11. Chains and additive set functions Appendix I. Vector and linear spaces Appendix II. Geometric and topological preliminaries Appendix III. Analytical preliminaries Index of symbols Index of terms
Product Description
This treatment of geometric integration theory consists of an introduction to classical theory, a postulational approach to general theory, and a section on Lebesgue theory. Covers the theory of the Riemann integral; abstract integration theory; some relations between chains and functions; Lipschitz mappings; chains and additive set functions, more. 1957 edition.
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